1 | // $Id: gcdp_s.tst,v 1.1.1.1 1998-04-17 15:07:40 obachman Exp $ |
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2 | |
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3 | // |
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4 | // gcdp_s.tst - short tests for gcd calculations mod p. |
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5 | // |
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6 | // Note: gcd(0, x) fails with a SEGV signal! |
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7 | // To Do: gcd calculations over transcendental extensions of |
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8 | // finite fields. |
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9 | // |
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10 | |
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11 | LIB "tst.lib"; |
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12 | tst_init(); |
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13 | tst_ignore("CVS ID : $Id: gcdp_s.tst,v 1.1.1.1 1998-04-17 15:07:40 obachman Exp $"); |
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14 | |
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15 | // |
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16 | // - ring r1=32003,x,dp. |
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17 | // |
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18 | |
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19 | ring r1=32003,x,dp; |
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20 | |
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21 | poly f=-9554*x^4-12895*x^3-10023*x^2-6213*x; |
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22 | poly g; |
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23 | |
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24 | // some trivial examples |
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25 | gcd(0, 0); |
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26 | gcd(0, 3123); |
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27 | gcd(4353, 0); |
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28 | |
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29 | // these examples fail so far!!! |
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30 | // gcd(0, f); |
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31 | // gcd(f, 0); |
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32 | |
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33 | gcd(23123, f); |
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34 | gcd(f, 13123); |
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35 | |
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36 | // some less trivial examples |
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37 | f=-9554*x^4-12895*x^3-10023*x^2-6213*x; |
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38 | g=-9554*x^3-3341*x^2+6213*x; |
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39 | gcd(f, g); |
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40 | |
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41 | f=-11265*x^6+12161*x^5+10369*x^4-12161*x^3+896*x^2; |
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42 | g=10669*x^8-10673*x^7+5*x^6+8*x^5-10681*x^4+10665*x^3+7*x^2; |
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43 | gcd(f, g); |
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44 | |
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45 | f=-7918*x^9-14406*x^8-7256*x^7+2092*x^6-2198*x^5-12539*x^4-14631*x^3-7150*x^2; |
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46 | g=-14833*x^13-7011*x^12+15121*x^11-10864*x^10+12943*x^9-9871*x^8+10354*x^7-1437*x^6+6604*x^5-10394*x^4-3231*x^3-9348*x^2-2092*x; |
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47 | gcd(f, g); |
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48 | |
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49 | f=106*x^13-583*x^12-1060*x^11+8056*x^10+1696*x^9-327*x^8+12508*x^7+8277*x^6+5609*x^5-12879*x^4+13144*x^3-2544*x^2; |
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50 | g=11118*x^14-5404*x^13-908*x^12-13908*x^11+3188*x^10-8818*x^9+10439*x^8-14811*x^7+15530*x^6-4891*x^5+6322*x^4+15829*x^3-13686*x^2; |
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51 | gcd(f, g); |
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52 | |
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53 | f=-14613*x^17+2235*x^16-298*x^15+4540*x^14+7214*x^13+5494*x^12-3122*x^11-4720*x^10+8300*x^9-6582*x^8-9908*x^7-15983*x^6-5802*x^5-8634*x^4+7899*x^3+10556*x^2+6931*x+11063; |
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54 | g=-10168*x^20+6674*x^19+3004*x^18+13113*x^17+9449*x^16+9097*x^15-6420*x^14+50*x^13+434*x^12-15226*x^11+3727*x^10-14065*x^9-9751*x^8-15792*x^7+6004*x^6-5059*x^5+2479*x^4-12504*x^3-11328*x^2-11338*x-8280; |
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55 | gcd(f, g); |
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56 | |
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57 | f=3812*x^22-6874*x^21+12586*x^20+3003*x^19-9568*x^18+11117*x^17 +7524*x^16+11138*x^15-9743*x^14+1892*x^13+12485*x^12-569*x^11-8265*x^10-5991*x^9+13701*x^8+2644*x^7-3936*x^6-15875*x^5+1289*x^4+3956*x^3-10099*x^2-6616*x+5401; |
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58 | g=10652*x^20-4144*x^19-11810*x^18+8237*x^17-8675*x^16+6545*x^15-3601*x^14+14559*x^13+8090*x^12-8378*x^11+14255*x^10+8767*x^9-13932*x^8+11602*x^7-10751*x^6-4899*x^5+8637*x^4+14084*x^3-11583*x^2+5882*x+885; |
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59 | gcd(f, g); |
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60 | |
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61 | // |
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62 | // - ring r2=(32003,a),x,dp. |
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63 | // |
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64 | |
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65 | ring r2=(32003,a),x,dp; |
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66 | minpoly=a^4+8734*a^3+a^2+11817*a+1; |
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67 | |
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68 | poly f=-9554*x^4-12895*x^3-10023*x^2-6213*x; |
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69 | poly g; |
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70 | |
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71 | // first, some of the above examples |
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72 | gcd(0, 0); |
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73 | gcd(0, 3123); |
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74 | gcd(4353, 0); |
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75 | |
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76 | // these examples fail so far!!! |
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77 | // gcd(0, f); |
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78 | // gcd(f, 0); |
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79 | |
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80 | gcd(23123, f); |
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81 | gcd(f, 13123); |
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82 | |
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83 | // some less trivial examples |
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84 | f=-9554*x^4-12895*x^3-10023*x^2-6213*x; |
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85 | g=-9554*x^3-3341*x^2+6213*x; |
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86 | gcd(f, g); |
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87 | |
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88 | f=-11265*x^6+12161*x^5+10369*x^4-12161*x^3+896*x^2; |
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89 | g=10669*x^8-10673*x^7+5*x^6+8*x^5-10681*x^4+10665*x^3+7*x^2; |
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90 | gcd(f, g); |
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91 | |
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92 | // now, examples involving the algebraic variable |
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93 | f=(25836*a^3*x^6+30467*a^2*x^6+26792*a*x^6+30467*x^6+27083*a^3*x^5+30808*a^2*x^5+28163*a*x^5+292*x^5+12440*a^3*x^4+19396*a^2*x^4+19616*a*x^4+23236*x^4+25156*a^3*x^3+31764*a^2*x^3+31235*a*x^3+6459*x^3); |
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94 | g=(14670*a^3*x^6+19715*a^2*x^6+22318*a*x^6+19715*x^6+19743*a^3*x^5+28179*a^2*x^5+19715*a*x^5+7335*x^5+6379*a^3*x^4+11397*a^2*x^4+23599*a*x^4+9861*x^4+16005*a^3*x^3+31525*a^2*x^3+30467*a*x^3+12918*x^3); |
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95 | gcd(f, g); |
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96 | |
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97 | f=(21147*a^3*x^5+10147*a^3*x^4+8142*a^2*x^4+27671*a*x^4+29289*x^4+29289*a^3*x^3); |
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98 | g=(6167*a^3*x^6+1536*a^2*x^6+5211*a*x^6+1536*x^6+17534*a^3*x^5+478*a^2*x^5+1536*a*x^5+19085*x^5+3203*a^3*x^4+26578*a^2*x^4+17052*a*x^4+26770*x^4+26002*a^3*x^3+24062*a^2*x^3+192*a*x^3+6386*x^3); |
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99 | gcd(f, g); |
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100 | |
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101 | f=(2295*a^2*x^11+5897*a^3*x^10+765*a^2*x^10+27718*a^3*x^9+1283*a^2*x^9+23792*a*x^9+518*x^9+22026*a^3*x^8+11468*a^2*x^8+16834*a*x^8+24778*x^8+28460*a^3*x^7+8140*a^2*x^7+28036*a*x^7+1613*x^7+18196*a^3*x^6+13274*a^2*x^6+4638*a*x^6+31194*x^6+12206*a^3*x^5+10349*a^2*x^5+30979*a*x^5+8612*x^5); |
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102 | g=(8192*a^3*x^10+8957*a^2*x^10+9659*a^3*x^9+28672*a^2*x^9+4553*a*x^9+12288*x^9+5819*a^3*x^8+320*a^2*x^8+14380*a*x^8+12104*x^8+12047*a^3*x^7+19823*a^2*x^7+6824*a*x^7+4335*x^7+29376*a^3*x^6+22190*a^2*x^6+31239*a*x^6+22647*x^6); |
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103 | gcd(f, g); |
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104 | $ |
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